Thank you very much for your lucid explanation. I think the series 1+delta^2+delta^4+delta^6+... ... ... is a gemetric series. Common ratio of any two consecutive terms=delta^2. Since 0
Hi Dr. Ozyurt, thank you for the detailed explanation. But I notice we should also prove the (D, D) is a SPNE, even though (D,D) is a NE of the stage game. Because player 1 may deviate from the NE if she find it is profitable in the future (similar to carrot and stick). According to my calculation, no one will deviate from (D, D) only if $\Delta$
There seems some mistake in your calculations because playing NE in every period is always SPNE, even if \delta is zero. By the way, this is true in all games.
@@selcukozyurt Thanks for your reply professor. My intuition is that if player 1 is very patient, let's say $\Delta$ is very big for player 1. If player 1 choose deviate to {C} at time $t$, the game will be triggered to (C, D), (D, C), (C, D), ..., with expected utility to be U_1(Deviation) = 0 + 3$\Delta$ + 0 + 3$\Delta$^3 + 0 + 3$\Delta$^5 +... = 3$\Delta$ / (1-$\Delta$^2). Comparing with non-deviation to play (D, D) forever, with U_1(Non-deviation) = 1 + $\Delta$ + $\Delta$^2 + ... = 1 / (1-\Delta). Deviation is a better response when Delta is large. What's the problem of this analysis? Thanks for helping me out.
Dear Sir, thank you so much for your videos. Excellent explanations clears all concepts so beautifully. Incredible. Watched so many and shall continue. I extremely Grateful 🙏 . If I pass would be because of your videos 🙏
First of all, thank you for these amazing videos. They have been of extreme support throughout my economics program. I have a doubt, however: Can tit for tat strategies form a SPNE when delta = 1/2? or they can never? It wasn't very clear for me. I mean, in this setup, is there a SPNE or not?
Thanks Professor! You always made the most difficult part much easier to comprehend and offered many distinctive and insightful observations.
Cant thank you enough about how you make my game theory course so much easier to understand. Thank you again!!
Thank you very much for your lucid explanation. I think the series 1+delta^2+delta^4+delta^6+... ... ... is a gemetric series. Common ratio of any two consecutive terms=delta^2. Since 0
I used the same method as you
Dear Professor, this video really helps me. thank you very much for your great explanation and effort!
Hi Dr. Ozyurt, thank you for the detailed explanation. But I notice we should also prove the (D, D) is a SPNE, even though (D,D) is a NE of the stage game. Because player 1 may deviate from the NE if she find it is profitable in the future (similar to carrot and stick). According to my calculation, no one will deviate from (D, D) only if $\Delta$
There seems some mistake in your calculations because playing NE in every period is always SPNE, even if \delta is zero. By the way, this is true in all games.
@@selcukozyurt Thanks for your reply professor. My intuition is that if player 1 is very patient, let's say $\Delta$ is very big for player 1. If player 1 choose deviate to {C} at time $t$, the game will be triggered to (C, D), (D, C), (C, D), ..., with expected utility to be U_1(Deviation) = 0 + 3$\Delta$ + 0 + 3$\Delta$^3 + 0 + 3$\Delta$^5 +... = 3$\Delta$ / (1-$\Delta$^2). Comparing with non-deviation to play (D, D) forever, with U_1(Non-deviation) = 1 + $\Delta$ + $\Delta$^2 + ... = 1 / (1-\Delta). Deviation is a better response when Delta is large. What's the problem of this analysis? Thanks for helping me out.
Best explanation EVER!
Dear Sir, thank you so much for your videos. Excellent explanations clears all concepts so beautifully. Incredible. Watched so many and shall continue. I extremely Grateful 🙏 . If I pass would be because of your videos 🙏
Very well explained!
First of all, thank you for these amazing videos. They have been of extreme support throughout my economics program. I have a doubt, however:
Can tit for tat strategies form a SPNE when delta = 1/2? or they can never? It wasn't very clear for me. I mean, in this setup, is there a SPNE or not?
Same question
Amazing!
Thanks!
Nb
Thanks a bunch 🤍